March 2020 - firedrake - imperial.ac.uk

fd.derivative
by Onno Bokhove 14 Apr '20

14 Apr '20

Dear Firedrakers, When taking a Firedrake (functional/form) derivative, say the derivative of the functional int (du/dx)^2 dx (plus some bc's) is the outcome the functional derivative (i) with or (ii) without integration by parts? I.e. is it: (ii) 2 int du/dx dv/dx dx or (i) -2 int d^2u/d x^2 v dx, modulo bc's, and with v = delta u? https://www.firedrakeproject.org/firedrake.html#firedrake.ufl_expr.derivati… (I am trying to understand why the below would work, and it does, with CG1 for X, or in the above with CG1 for v and u, which only can work when no ibp is done. ) Kind regards, Onno PS: # Kinematics # Right Cauchy-Green tensor if self.nonlin: d = self.X.geometric_dimension() I = fd.Identity(d) # Identity tensor F = I + fd.grad(self.X) # Deformation gradient C = F.T*F E = (C-I)/2. # Green-Lagrangian strain # E = 1./2.*( fd.grad(self.X).T + fd.grad(self.X) + fd.grad(self.X).T * fd.grad(self.X) ) # alternative equivalent definition else: E = 1./2.*( fd.grad(self.X).T + fd.grad(self.X) ) # linear strain self.W = (self.lam/2.)*(fd.tr(E))**2 + self.mu*fd.tr( E*E ) # f = fd.Constant((0, 0, -self.g)) # body force / rho # T = self.surface_force() # Total potential energy Pi = self.W * fd.dx # Compute first variation of Pi (directional derivative about X in the direction of v) F_expr = fd.derivative(Pi, self.X, self.v)

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Re: [firedrake] Firedrake in a project at ATI
by Ham, David A 24 Mar '20

24 Mar '20

Dear Eric, Thanks for the email. Since you indicated that you tried to join the mailing list, I have taken the liberty of subscribing you to the list and copying the list in on my answer. We currently have what you want for the cases of point evaluation node elements (i.e. CG and DG elements). See: https://www.firedrakeproject.org/interpolation.html#interpolator-objects . The interpolator object contains the interpolation matrix in appropriate cases. There are people working on generalising this to all the elements we have, and making the differentiation work cleanly so that things like point forcing and point measurements work seamlessly. I hope we have more progress on this in the coming months. Cheers, David -- Dr David Ham Department of Mathematics Imperial College London https://www.imperial.ac.uk/people/david.ham From: Eric Daub <edaub(a)turing.ac.uk> Date: Wednesday, 11 March 2020 at 12:19 To: "Ham, David A" <david.ham(a)imperial.ac.uk> Subject: Firedrake in a project at ATI Dear David, I am an RSE at the Turing working with Mark Girolami (and Alastair Gregory before he moved to a new position) on implementing a probabilistic version of the Finite Element Method that he has developed over the past couple of years. The method provides a Bayesian framework for finding FEM solutions conditioned on sensor data, and Mark hopes that this tool will become a part of several research projects in the Turing Data-Centric Engineering Programme. Some other ICL researchers (Craig Buchanan and Leroy Gardner in Civil Engineering) are also involved with this research program. I am building our software on top of Firedrake as suggested by Alastair, as it nicely supports much of what we need to do straight out of the box (in particular, easily integrating with PETSc and ensemble parallelism have made my job relatively straightforward, as those have proven to be the difficult bits of the implementation thus far). However, one additional piece that is necessary for the FEM solves required by the method is the ability to access the matrix that interpolates between the FEM DOF nodes and arbitrary sensor locations where data has been collected. This involves evaluating the FEM basis functions at all of the sensor locations and collecting them in a sparse matrix. I did not see a simple way to do this using the existing interfaces, but it is highly likely that I missed something. I have a simplified version that works for linear CG elements on triangular/tetrahedral meshes that I have been using for testing purposes, but eventually want to implement this for the more general case. Any advice on how to proceed would be greatly appreciated. I attempted to join the Firedrake listserver, as I suspect that some of the discussions arising there may be relevant to my work, though it seems that my request never went through. If I can join the list I would be happy to re-pose my question there for the development team if you feel that would be more appropriate. Thanks for your help, and I hope that my work can help get more people using Firedrake in various research threads here at the Turing. Cheers, Eric The Alan Turing Institute is a limited liability company, registered in England with registered number 09512457. Our registered office is at British Library, 96 Euston Road, London, England, NW1 2DB. 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Returning eigenvectors of a solution to a PDE at each node
by Andrew Hicks 20 Mar '20

20 Mar '20

Hello, I am currently using firedrake to solve a PDE. The solution to this PDE is vector-valued, and I have no problem finding the solution. However, I'd like to go a step further. I have named the solution "q_soln" and this is a 2-dimesional vector. I have used this vector to construct a 2x2 matrix at the node [0.5,0.5]. I then extracted an eigenvector from this matrix, and then I printed it: import numpy as np from numpy import linalg as la E1 = (1 / np.sqrt(2)) * np.array([[1,0],[0,-1]]) E2 = (1 / np.sqrt(2)) * np.array([[0,1],[1,0]]) # as an example, we evaluate the solution at the point [0.5,0.5], and pick the first eigenvector q_soln_atpoint = q_soln.at([0.5,0.5]) Q_soln = q_soln_atpoint[0] * E1 + q_soln_atpoint[1] * E2 evals, evecs = la.eig(Q_soln) # evec is a 2x2 array with the columns being the e-vectors q_soln_evec = np.zeros((1,2)) q_soln_evec += evecs[0,:] print(q_soln_evec) My question is this: how can I get firedrake to do this automatically for every node in my mesh, and then store it in as a Function "q_soln_evec"? The only reason I used numpy to get this one point is because I'm unfamiliar with firedrake. I bet firedrake has some built-in way of doing what I need here. Thanks, Andrew Hicks

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Getting on mailing list
by Andrew Hicks 19 Mar '20

19 Mar '20

I cannot seem to get on the mailing list. I entered my email (ahick17(a)lsu.edu<mailto:ahick17@lsu.edu>) into the system two different times, expecting a confirmation email, but never received one. I am now attempting to email the list directly. Andrew Hicks

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Solving Decoupled Problems over Elements of Mesh of Global Problem
by Austin Kaul 12 Mar '20

12 Mar '20

Hello, I am working on developing a method where optimal discontinous test functions are computed for the global problem. The issue is that these optimal test function computations are decoupled from the global problem and are over each element individually. Has this been done or is there a way with par_loop() to perform a solve over each element of a mesh and have its solutions contribute to the global solve at the end? Each element problem has its own variational statement with its own test functions which we would define. Using these results we would construct the global stiffness matrix(function) as we solve this optimal test function problem over each element. We have implemented a very simple version of this with an in house code but your framework allows for so much flexibility we would love to be able to do this in Firedrake. Regards, -- Austin Kaul

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Making Conditional BC beyond the Conditional Statement
by Austin Kaul 09 Mar '20

09 Mar '20

I am implementing a space time simulation of the Cahn-Hilliard equation with a stable FE method called AVS-FE. I am using the z dimension as the time variable of the problem. I am running into issues when implementing a Dirichlet boundary condition. I need to implement a piecewise continuous function over one of my boundaries with more than 2 values which is why I cannot use the conditional statement. I have searched around and found this has not been done much and am getting errors I do not understand. Attached is the python script that I run which functions for a simple boundary condition but not the more complex one I am trying to implement with an Expression call. If I could get assistance with this error as to why my expression is not working properly it would be appreciated. The error I am getting is: Traceback (most recent call last): File "/home/austin/firedrake/src/firedrake/firedrake/interpolation.py", line 76, in interpolate assembled_interpolator = self.frozen_assembled_interpolator AttributeError: 'Interpolator' object has no attribute 'frozen_assembled_interpolator' During handling of the above exception, another exception occurred: Traceback (most recent call last): File "cahn_hilliard_prototype.py", line 224, in <module> u_source.interpolate(MyExpression_t0()) File "/home/austin/firedrake/src/firedrake/firedrake/function.py", line 349, in interpolate return interpolation.interpolate(expression, self, subset=subset) File "/home/austin/firedrake/src/firedrake/firedrake/interpolation.py", line 34, in interpolate return Interpolator(expr, V, subset=subset, access=access).interpolate() File "/home/austin/firedrake/src/firedrake/firedrake/interpolation.py", line 79, in interpolate assembled_interpolator = self.callable() File "/home/austin/firedrake/src/firedrake/firedrake/interpolation.py", line 170, in callable l() File "/home/austin/firedrake/src/PyOP2/pyop2/base.py", line 3563, in compute self._compute(iterset.core_part, fun, *arglist) File "/home/austin/firedrake/src/PyOP2/pyop2/pyparloop.py", line 114, in _compute raise NotImplementedError NotImplementedError I don't understand the frozen assembled interpolator part which is the problem I believe. Regards, -- Austin Kaul

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Advertising offer for firedrakeproject.org
by Samantha Stone 05 Mar '20

05 Mar '20

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Installation Help
by McCash, Luthais 02 Mar '20

02 Mar '20

Hello, I’m currently trying to install Firedrake on my mac and having numerous issues. Perhaps you can advise – I’m very new to these platforms so any guidance you can provide I’d be grateful. Best, Luthais McCash Honorary Industrial Fellow College of Science & Engineering, University of Leicester, University Road, Leicester, LE1 7RH, UK e: lm460(a)leicester.ac.uk<mailto:cjd21@le.ac.uk> w: www.le.ac.uk<https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.le.ac.…> [A2q05NIZyAsAAAAASUVORK5CYII=] Follow us on Twitter<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Ftwitter.c…> or visit our Facebook<https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.facebo…> page This email and any files transmitted with it are confidential. If you are not the intended recipient please accept our apologies; please do not disclose, copy, or distribute information in this email nor take any action in reliance on its content: to do so is strictly prohibited and may be unlawful. Please inform us that this message has gone astray before deleting it. Thank you for your co-operation.

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